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### Thue Equation

A Thue equation is a Diophantine equation of the formin terms of an irreducible polynomial of degree having coefficients for which solutions in integers and are sought for each given constant with .Thue (1909) proved that such an equation has only finitely many solutions, but it was not until much later that Tzanakis and de Weger (1989) gave a practical algorithm for finding bounds on and . Although these bounds can be astronomically large in some cases, they are typically small enough to allow an exhaustive search for all solutions.

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